PBW-deformations of N-Koszul algebras

Details PBW-deformations of N-Koszul algebras PBW-deformations of N-Koszul algebras

2005-05-26

arxiv.org/abs/math/0505570v2

Journal of Algebra 302, (2006), no.1, p.116-155

Mathematics

Rings and Algebras

35 pages. Some minor corrections

Scientific paper

10.1016/j.jalgebra.2005.08.032

For a quotient algebra $U$ of the tensor algebra we give explicit conditions on its relations for $U$ being a PBW-deformation of an $N$-Koszul algebra $A$. We show there is a one-one correspondence between such deformations and a class of $A_\infty$-structures on the Yoneda algebra $Ext_A^*(k,k)$ of $A$. We compute the PBW-deformations of the algebra whose relations are the anti-symmetrizers of degree $N$ and also of cubic Artin-Schelter algebras.

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